The value of the four integers are; Triangle = 1; Diamond = 5; Square = 2; Clubsuit = 7
<h3>How to solve simultaneous equations?</h3>
We are given the equations;
Triangle + Triangle + Triangle + Triangle + Triangle = Diamond
Triangle + Square + Square = Diamond
Square + Diamond = Clubsuit
If triangle is T, Diamond is D, Square is S and Clubsuit is C, then we have;
5T = D ..... (eq 1)
T + 2S = D .... (eq 2)
S + D = C ......(eq 3)
Equations (1) and (2) are equal. Thus;
5T = T + 2S
4T = 2S
2T = S
T = S/2
Put T + 2S for D in equation (3):
S + T + 2S = C
3S + T = C
3S + S/2 = C
7S/2 = C
Since they are all integers from 1 to 9, it means that T cannot be more than 1 because 5T = D. Thus; T = 1
1 = S/2
S = 2
C = 7 * 2/2
C = 7
D = 5
Read more about Simultaneous equations at; brainly.com/question/148035
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Answer:
There are two rational roots for f(x)
Explanation:
We are given a function
f(x) = x^6-2x^4-5x^2+6f(x)=x6−2x4−5x2+6
To find the number of rational roots for f(x).
Let us use remainder theorem that when
f(a) =0, (x-a) is a factor of f(x) or x=a is one solution.
Substitute 1 for x
f(1) = 1-2-5+6=0
Hence x=1 is one solution.
Let us try x=-1
f(-1) = 1-2-5+6 =0
So x =-1 is also a solution and x+1 is a factor
We can write f(x) by trial and error as
f(x) = (x-1)(x+1)(x^2-3)f(x)=(x−1)(x+1)(x2−3)
We find that f(x) (x^2-3)f(x)(x2−3) factor gives two irrational solutions as
±√3.
Hence number of rational roots are 2.
There are several types of keboard designs and research is ongoing to improve their efficiency e,g QWERTY, QWERTZ and AZERTY keyboards
<h3>Types of Keyboards</h3>
Bellow is an extended list of the various types of keyboards
- Qwerty Keyboards
- Wired Keyboards
- Numeric Keypads
- Ergonomic Keyboards
- Wireless Keyboards
- USB Keyboards
- Bluetooth Keyboards
Learn more about the types of keyboards here:
brainly.com/question/13380788
Explanation:
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